Abstract:The identification of linear systems from input and output observations is an important and well-studied topic. When both the input and output observations are noisy, the resulting problem is sometimes called the "errors in variables" problem. Existing work on this problem deals with the identification of multivariate systems and thus results in algorithms that are necessarily somewhat complex and often involve iteration. In this report we treat an important special case of the problem: estimation of a system bias and a system gain from noisy observations of system input and output. In addition, we invoke an input-output noise power ratio constraint. This constraint can also be interpreted as a parameter that moves the problem in a continuous fashion between two limiting cases, each of which is a conventional least-squares problem. We do not model the input signal, and we place minimal restrictions on the input and output observation noises. We develop five different low-complexity closedform solutions to the problem. The final two are the most satisfying and we explore these further through simulations. Our original motivation for working on this problem came from the need to calibrate objective and subjective estimates of perceived video or speech quality. We expect that our solutions may also find applications in remote sensing, active noise reduction, echo cancellation, channel estimation, and channel equalization.

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